Authors:
Bernd Steinbach
1
and
Christian Posthoff
2
Affiliations:
1
Freiberg University of Mining and Technology, Germany
;
2
The University of the West Indies, Trinidad and Tobago
Keyword(s):
Artificial Intelligence, Creativity, State Space Search, Constraint Satisfaction, Four-valued Edge Coloring, Complete Bipartite Graph, Rectangle-free Grid, Boolean Equation, SAT-solver, XBOOLE.
Related
Ontology
Subjects/Areas/Topics:
AI and Creativity
;
Artificial Intelligence
;
Constraint Satisfaction
;
Knowledge Representation and Reasoning
;
Soft Computing
;
State Space Search
;
Symbolic Systems
Abstract:
The topic of this paper is the rectangle-free coloring of grids using four colors which is equivalent to the edge
coloring of complete bipartite graphs without complete monochromatic subgraphs K2,2. So far unsolved are
the grids of the sizes 17×17, 17×18, 18×17, and 18×18. The number of different 4-color patterns of the
grid 18×18 is equal to 4324 ≈ 1.16798∗10195. We summarize in this paper some basic approaches in order to
gain the required knowledge. Three creative approaches are steps so solve the most complex grid of the size
18×18. Two advanced creative approaches reduce the required runtime to less than 12 percent.